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Related Rates Day 1. Related Rates… Rates of change of two or more related variables that are changing with respect to time. Related Rates… When two or more related variables are changing with respect to time. Given: y = x 2 + 3 and when x = 1, find when x = 1.

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Related Rates Day 1


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slide2
Related Rates…Rates of change of two or more related variables that are changing with respect to time.

Related Rates…

When two or more related variables are changing with respect to time.

write the following statements mathematically
Write the following statements mathematically
  • John’s height, h, is changing at the rate of 3 in./year
  • The volume of a cone, V, is decreasing by 2 in3/min.
  • The radius of a circle, r, in increasing at 4 ft. per hour
a rectangle has length l and width w
A rectangle has length l and width w.
  • Write an equation to represent the rate of change of the perimeter.
  • What is the rate of change of the perimeter if the length is increasing at 2 inches /min. and the width is decreasing 3 inches/min.?
a rectangle has length l and width w1
A rectangle has length l and width w.
  • Write an equation to represent the rate of change of the area.
  • If the length is decreasing at 2 inches /min. and the width is increasing 1.5 inches/min., What is the rate
  • of change of the area when the length is 10 and the
  • width is 4?
related rates in general
Related Rates…in general

True all of the time

At the instant…

slide8

Air is being pumped into a spherical balloon at the rate of 4.5 cubic inches per minute. Find the rate of change of the radius when the radius is 2 inches.

True all of the time

At the instant…

slide9

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius of the outer ripple is increasing at a constant rate of 1.2 feet per second. When the radius is 4 feet, at what rate is the total area of the disturbed water changing?

True all of the time

At the instant…

slide10
All edges of a cube are expanding at the rate of 5 cm/sec. How fast is the surface area changing when the length of each edge is 12 cm?

True all of the time

At the instant…

slide11

A 20 ft long ladder is leaning against a wall and sliding toward the floor. If the foot of the ladder is sliding away from the base of the wall at a rate of 10 ft/sec, a) how fast is the top of the ladder sliding down the wall when the top of the ladder is 12 ft. from the ground? b) find the rate at which the angle between the ladder and the wall is changing when the top of the ladder is 12 ft. from the ground?

slide12

A girl 4 feet tall walks at a rate of 1.5 ft/sec away from a light that is 10 feet above the ground. At what rate is the length of her shadow changing when she is 8 feet from the base of the light?

slide13

Suppose senior board decided to throw a graduation bash and the coca cola is flowing freely from the bottom of a giant cone-shaped barrel which is 12 feet deep and 6 feet in radius at the top. If the coke is disappearing at a rate of 6 cubic feet per hour, at what rate is the depth of the coke in the tank going down when the depth is 4 feet?